Majorana fermions (non-Abelian anyons) appear as edge states in the topological phase of the Kitaev wire, and are naturally immune to static disorder. I discuss the effects of a classical noise ("time-dependent disorder") on the Majorana edge correlations, and on the fidelity of braiding operations for both global and local noise in the chemical potential. While in general noise will induce heating and dephasing, it is still possible to have long-lived quantum correlations in the presence of fast noise due to motional narrowing, even when the noise drives the system rapidly between the topological and non-topological phases.